Fundamentals of Sensors

This page aims to present relevant general knowledge and background on MEMS sensors and other IC sensors, as well as on signal processing and metrology, to make it easier to write sensor drivers and to use them.

Digital-Output IC Sensors

Digital-output IC sensors are mixed-signal integrated circuits that measure an analog physical quantity and expose the result as digital values. Many of such sensors are micro-electromechanical sensors (MEMS) sensors. MEMS technology allows them to be very small in size, and to fit both the sensing element and the digital logic into a single package. Because MEMS sensors are sensitive to temperature, they often comprise temperature sensing elements for compensation, even if their primary function is not to measure temperature. These temperature-sensing elements may have an accuracy of only a few degrees, but that is sufficient for temperature compensation.

Digital-output IC sensors use, in the general case, the following architecture:

Some sensors’ datasheets do describe their architecture, but sometimes omit some elements, especially the filters.

Anti-Aliasing Filters and Bandwidth

In continuous mode, the rate at which the sensor’s digital interface refreshes its values is called the output data rate (ODR) and is generally configurable. Depending on the sensor, the ODR may only downsample the digital output, or it may change the sampling rate of the ADC. If the sampling rate of the ADC is variable, there must generally be an analog low-pass filter (LPF) upstream of it, that acts as an anti-aliasing filter. The cutoff frequency of that low-pass filter must be adjusted based on the sampling rate. In some cases, the low-pass filter may not be an electronic filter: for instance the thermal inertia of a temperature sensor’s package acts as a low-pass filter and might be sufficient. In addition, if there is a digital downsampler, that reduces the rate of digital samples output by the sensor, there must also be a digital low-pass filter to avoid aliasing.

Note

A downsampler is also called a decimator, which may or may not also include an anti-aliasing filter.

The anti-aliasing filters (AAF) are required because, if the signal contains frequencies higher than half the sampling rate or the ODR (i.e., higher than the Nyquist frequency), aliases of these will appear as extraneous low frequencies in the output. AAFs are low-pass filters whose function is to suppress the signal’s frequencies higher than the Nyquist frequency, to prevent aliases from appaearing.

Being low-pass filters, these filters remove high-frequency components, which may be desired if they constitute noise. On the other hand, if the signal is high bandwidth, i.e., if high frequencies are actually desired, both the cutoff frequencies of these filters and the sampling rate and ODR must be kept high enough, to preserve these high frequencies through the chain, according to the Nyquist–Shannon sampling theorem.

Precision, Effective Resolution, and Oversampling

Precision refers to how close measurement results of a sensor are to each other, for a given true value. It characterizes random errors marring the measurement results. It is commonly modeled as noise in datasheets.

A related concept is the effective resolution, which is essentially the number of bits of the output that are not marred by random errors. It is not to be confused with just “resolution,” which is simply the number of bits of the output. For instance, a 12-bit ADC always generates 12 bits, but fewer than that are likely noise-free.

To improve the precision of sensors, a common technique is oversampling, which involves taking repeated measurements and averaging them, to cancel out some of the noise and therefore increase the effective resolution. Many sensors support built-in oversampling, and can be set to automatically trigger multiple measurements and average them. Oversampling can also be implemented in software, on the microcontroller. A potential drawback of averaging is that it behaves as a low-pass filter, and therefore reduces the sensor bandwidth (i.e., its ability to measure high frequencies), which may be undesired.

Sensitivity

Sensitivity, as commonly used in datasheets, is the smallest change in value that can be reflected on the output. It is related to the resolution: a higher resolution allows for a higher sensitivity. As the resolution (i.e., the number of bits in the output) is generally fixed, sensors often have a setting to reduce the sensitivity to allow outputting a greater range of values. This may be implemented in the analog domain using a programmable-gain amplifier (PGA) upstream of the ADC. A better term for this meaning of sensitivity would be responsivity.

Note

Sensitivity is also sometimes defined as taking precision into account, in which case a higher effective resolution is required for a higher sensitivity.

Trueness and Accuracy

Trueness has been introduced by ISO 5725-1 to refer to how close the mean of measurement results of a sensor is to the true value. It characterizes systematic errors and is generally described as an offset in datasheets. Trueness is also commonly referred to as accuracy. However, in ISO 5725-1, accuracy instead encompasses both trueness and precision. Repeating the measurement does not help improve the trueness, but some systematic errors may be eliminated through calibration. In the context of sensors, a common source of inaccuracy is temperature: that is why many IC sensors embed temperature sensing elements to allow for temperature compensation, either in the sensor itself or in software.

Note

Note that in general, the accuracy of a sensor and of a system comprising that sensor are not the same. For instance, in a digital thermometer (a system using a temperature sensor), the heat generated by the system may influence the sensor, thus reducing the system accuracy without further calibration.